Scientific Journal of KubSAU

In this article, we discuss various issues related to the formulas approximating the distribution function of prime numbers pi(x). This question has occupied many scholars, but the exact function is well approximated function pi(x) over the number of positive integers not. Based on certain hypotheses, we present a new function s(x) is very well approximated pi(x). The above article hypotheses are so important that their numerical validation and refinement for the lengths of the segments more in 1014 - one of the main areas related to the problem of approximation of the function pi(x) throughout the series of natural numbers. After analyzing the behaviors and constructs many functions, we are building the basis of the function s(x), which is well approximates the function pi(x) throughout the series of natural numbers. We also present a table of values for x, less or equal 1022 for the difference of s(x) - pi(x)